Green Arrow and Batman always have had that sense of tension, years before the retro story in "Identity Crisis." Some of it is philosophical.
Green Arrow is less reactionary than the other members of The Justice League. Green Arrow is not above using lethal force to take out villains such as Prometheus. He also has shown trying to deal with higher-level social concepts, such as racism and drug wars. He sees The Justice League as being able to do more on the street with their superpowers and abilities.
Batman, on the other hand, is an authoritative figure when it comes to dictating to other superheroes. Batman sets rules for other members of The Justice League and another set of rules for himself (like leaving and not joining in missions when he feels like it). Green Arrow is much more of a free-flowing person who chafes under such restrictions, and is one of the few Justice League members who stands up to Batman's selective dogma.
In some ways, Green Arrow sees Batman as self-serving and hypocritical -- he knows how life is for people in crime-infected areas yet does nothing to stop corruption until it reaches a certain stage. For instance, Green Arrow is someone who would try to kill The Joker, especially given how much pain The Joker inflicted on Gotham City and Batman personally. Yet Batman continually repeats locking up The Joker in Arkham Asylum and waits until he escapes again.
Additionally, some of that contempt is based on how similar they are to each other. Batman and Green Arrow are street-level superheroes who use their skills and resources to fight crime and address villains the more powerful heroes rarely address. Both men are stubborn with complicated relationships with their respective inner circles.
However, when it comes to certain situations Batman shows he will trust Green Arrow. They seem to have a begrudgingly mutual respect. In that context, they are an example of two people who don't get along because they see too much of themselves in the other person.